Solve for $x$. $5^x=5^3\cdot5^8$ $x=$
Solution: When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${5^x}={5^3}\cdot5^8}$. $\begin{aligned} &={\underbrace{5\cdot5\cdot5}_\text{3 times}}\cdot\underbrace{5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5 \cdot 5\cdot5}_\text{8 times}} \\\\\\ &={\underbrace{5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot5\cdot5\cdot5}_{x\text{ times}}} \\\\ \end{aligned}$ $x=11$